Some immediate, fundamental consequences of my work with Menikoff and Sharp at Los Alamos were also published during the 1980s. In 1983, we presented a rigorous kinematical framework for the fractional spin of anyons, including the first (as far as I can determine) explicit identification of the braid group \(B_N\)  as the homotopy group whose unitary representations govern \(N\) -anyon exchange statistics [1]}, [2]}. In 1985 we first predicted nonabelian anyons [3]}, described by wave functions equivariant under higher-dimensional unitary representations of \(B_N\) . This parallels the earlier idea of parastatistics for particles in \(\mathbb {R}^3\) , where the homotopy group is \(S_N\) . We also pointed out in 1985 that systems of distinguishable particles in two-space are described by wave functions equivariant for the group of colored braids. These wave functions can pick up intermediate phases as particles fully circle each other, without exchange. Our conclusion about nonabelian anyons was contrary to the expectation expressed by Wu in 1984 [4]} that a “general theory” would include only one-dimensional representations of the braid group; we published it as a response to Wu's paper.
